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We consider the plurality consensus problem among $n$ agents. Initially, each agent has one of $k$ different opinions. Agents choose random interaction partners and revise their state according to a fixed transition function, depending on…
This contribution is concerned with mathematical models for the dynamics of the genetic composition of populations evolving under recombination. Recombination is the genetic mechanism by which two parent individuals create the mixed type of…
We give efficient protocols and matching accuracy lower bounds for frequency estimation in the local model for differential privacy. In this model, individual users randomize their data themselves, sending differentially private reports to…
This article presents a theoretical investigation of computation beyond the Turing barrier from emergent behavior in distributed systems. In particular, we present an algorithmic network that is a mathematical model of a networked…
We consider the new extension of population protocols with unordered data and show that the corresponding well-specification problem and therefore also other verification problems are undecidable.
Opacity is a generic security property, that has been defined on (non probabilistic) transition systems and later on Markov chains with labels. For a secret predicate, given as a subset of runs, and a function describing the view of an…
We propose a probabilistic quantum protocol to realize a nonlinear transformation of qutrit states, which by iterative applications on ensembles can be used to distinguish two types of pure states. The protocol involves single-qutrit and…
I survey our recent work on the verification of population protocols and their state complexity.
Two pure orthogonal quantum states can be perfectly distinguished by sequential local action of multiple pairs of parties. However, this process typically leads to the complete dissolution of entanglement in the states being discriminated.…
The bifurcation theory of ordinary differential equations (ODEs), and its application to deterministic population models, are by now well established. In this article, we begin to develop a complementary theory for diffusion-like…
When dealing with process calculi and automata which express both nondeterministic and probabilistic behavior, it is customary to introduce the notion of scheduler to solve the nondeterminism. It has been observed that for certain…
The \emph{rational fair consensus problem} can be informally defined as follows. Consider a network of $n$ (selfish) \emph{rational agents}, each of them initially supporting a \emph{color} chosen from a finite set $ \Sigma$. The goal is to…
In this work, we study protocols so that populations of distributed processes can construct networks. In order to highlight the basic principles of distributed network construction we keep the model minimal in all respects. In particular,…
This paper is concerned with the evolution of haploid organisms that reproduce asexually. In a seminal piece of work, Eigen and coauthors proposed the quasispecies model in an attempt to understand such an evolutionary process. Their work…
Designing fair algorithmic decision systems requires balancing model performance with fairness toward affected individuals: More fairness might require sacrificing some performance and vice versa, yet the space of possible trade-offs is…
We consider a general class of birth-and-death processes with state space $\{0,1,2,3,\ldots\}$ which describes the size of a population going eventually to extinction with probability one. We obtain the complete spectrum of the generator of…
In using observed data to make inferences about a population quantity, it is commonly assumed that the sampling distribution from which the data were drawn belongs to a given parametric family of distributions, or at least, a given finite…
We propose a new theoretical model for passively mobile Wireless Sensor Networks. We call it the PALOMA model, standing for PAssively mobile LOgarithmic space MAchines. The main modification w.r.t. the Population Protocol model is that…
We study the density estimation problem defined as follows: given $k$ distributions $p_1, \ldots, p_k$ over a discrete domain $[n]$, as well as a collection of samples chosen from a ``query'' distribution $q$ over $[n]$, output $p_i$ that…
We investigate space-time trade-offs for population protocols in sparse interaction graphs. In complete interaction graphs, optimal space-time trade-offs are known for the leader election and exact majority problems. However, it has…